This is a multi-center, open-label study to evaluate the activity and safety of the protease inhibitor indinavir sulfate (MK-0639) administered in combination with the nucleoside analogue inhibitors of reverse transcriptase zidovudine (ZDV) and lamivudine (3TC) for the treatment of acute HIV infection. These newly infected subjects harbor virus with the least genetic diversity and are therefore most likely to be drug responsive. The patients recruited in the first year of the study will be allowed to continue to participate in this study with yearly extensions for an indefinite period. The drug therapy in the extension phase of this study will remain unchanged: MK-0639 at 800 mg q8h, ZDV at 200 mg q8h, and 3TC at 150 mg BID. Safety will be assessed as well as antiviral activity, which will be determined by serial measurements of plasma RNA and cell-associated virus, as measured by quantitative co-culture.